Project Background: Monitoring veterans'health care requires use of longitudinal data. The VA health care system has an extremely rich and high-dimensional longitudinal data on a large number of subjects who become a user at an earlier age and stay with system for the rest of their life. This data provides some unique observational longitudinal cohorts on variety of diseases and their management strategies. For learning from these observational longitudinal data appropriate methodologies for dimension and confounding bias reduction are required. Project Objectives: The proposed research will develop a model for estimating the effect of a grouping variable (intervention) when we are faced with a dynamic situation. Under this setup, our objectives then are: 1. How to reduce the high dimension of these repeated measure covariates, so that no information is lost with respect to the outcome and the grouping variable (intervention)? 2. How to extract and estimate the time-dependent effect of the intervention from the confounding effect of these covariates? Project Methods. To achieve dimension reduction and covariate balance, we construct sufficient summaries. A sufficient summary is a parametric function of the covariates that given any of its values, the covariate distribution is free from intervention level. In order to find a sufficient summary, we should know the density ratios of the covariates given different levels of the intervention. When we have repeated measures these density ratios are extremely difficult to be specified realistically. To simplify the model without losing its description of reality, we make two assumptions: 1. Response, the intervention and the covariate values at each visit (time point) depend on their corresponding the recent past values (this is called Markov property of order one). 2. The value of each of these three variables at a given visit may only depend on the status of the other variables at that visit. This pair of assumptions has a Hidden Markov Chain structure. Then, we derive sufficient summaries for some very important cases. Next, we define the causal effect of the intervention. This is the effect of the intervention had the covariates were independent of the intervention. We show that this effect can be calculated only using the sufficient summaries. Finally, since this effect depends on the parameters of the model, in order to estimate this effect at all time points, we assume the parameters as a function of time have some Dynamic Bayes Markovian structures. We will apply restricted maximum a posteriori method to estimate the parameters and, hence, the effect function, recursively. Importance to VA: In developing methods that lead to improved, more reliable inference in epidemiological, clinical, and health services research, the proposed study will lead to more soundly established medical interventions and health programs that will directly impact veteran's health. Over the course of numerous such research studies the cumulative impact of this research could be substantial.
Conducting randomized clinical trials is not always feasible or even possible. The VA Health Care System constantly records, updates and monitors a large panel of patients with a vast variety of medical conditions and treatment services. Developing statistical meth- ods that provide approximate alternatives to the more expensive longitudinal randomized designs are necessary. Classical longitudinal analysis of an observational panel of subjects with long history of large number of imbalanced covariates cannot produce unconfounded eect estimates for the intervention. Our aim is to provide a methodology for analysis of longitudinal observational data that by replacing the high-dimensional covariates with a low-dimensional balancing summary identies strata of patients within which intervention assignment is approximately at random and,hence reduced-bias estimates are possible. 1